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تحت إشراف قسم الرياضيات والإحصاء أقيم يوم الأحد الموافق 16/7/1442هـ  سيمنار بعنوان:

                                               Uniformly Connected Graphs

قدمته د. نسرين المهنا وذلك في تمام الساعة 2:00 مساءً عبر برنامج الزووم.

Abstract:

Perhaps the most fundamental property that a graph can possess is that of being connected. Two vertices u and v of a graph G are connected if G contains a u − v path. The graph G itself is connected if every two vertices of G are connected. The well- studied concept of connectivity provides a measure on how strongly connected a graph may be. There are many other degrees of connectedness for a graph. A Hamiltonian path in a graph G is a path containing every vertex of G. Among the best-known classes of highly connected graph are the Hamiltonian-connected graphs, in which every two vertices are connected by a Hamiltonian path.

    In the present talk, we introduce the new concept of uniformly connected graphs which combines several features of connectedness of graphs in the literature. More precisely, for a positive integer k, a nontrivial connected graph G is k-uniformly connected if every two vertices of G are connected by a path of length k. The uniform spectrum of G is the set of all positive integers k for which G is k-uniformly connected.